It was his wife Soumaya, Mr Slim says, who really taught him about sculpture and paintings.

“She was very sensitive to art,” he explains. “For our honeymoon we went to lots of galleries. The first time I went to Europe, in 1964, I went to galleries alone. In the UK, the British Museum, the National Gallery, and I loved the National History Museum. That was 1964.

"Then in 1966 was my honeymoon, and we also went to England. We went to Greece, New York, then we went by boat to Naples, Spain, France. It was about 40 days, seeing different places, cities, countryside.”

On their return, the couple attended an auction to buy furniture for their new house. And it was then that Mr Slim purchased his first painting – a 16th-century Flemish work, showing a scene of lions and Christians battling the Moors. Although it was an anonymous work, not considered a great piece, it hung in the kitchen as he wanted to look at it all the time.

This was to lay the foundations for the Museo Soumaya, which will launch with a glittering cocktail party.

All of the heads of state from Latin American countries have been invited, and guests will include Larry King, Colombian author Gabriel García Márquez, fashion designer Oscar de la Renta, Queen Noor of Jordan, former Spanish president Felipe González, his friends the Rothschilds, and hopefully Bill Clinton, with whom Mr Slim has launched a series of charitable initiatives.

“When you buy a collection, you have to exhibit it,” he says, as we drive towards the museum. “You have to share it. When I started buying art, in Mexico the museums didn’t have many European works. Periodically there would be exhibitions that came to Mexico, but it was a small percentage of the total art on show.

“So that was when I began to buy European art. And also the prices were very different – it’s not like now, when they are so high, unimaginably high.

“Now those people who can’t travel abroad have somewhere they can go to see great European art. That was the thinking behind buying European art.”

The museum will house over 66,000 pieces, mainly European and Mexican art. From Cézanne to Renoir, Van Gogh to Matisse, da Vinci to Rivera, the jaw-dropping collection is the result of many years of passionate study and accumulation.

It also includes the world’s largest collection of pre-Hispanic and colonial coins, plus a vast collection of letters and historical documents. Visitors will be able to read Christopher Columbus’s letters, or study the writings of Hernán Cortés and the Catholic Kings of Spain.

For the past 16 years, the collection has been housed in a museum in the south of the capital. Its director, Alfonso Miranda, put the value at easily over $700 million (£435 million).

The new museum will be an enormous structure designed by Mr Slim’s son-in-law Fernando Romero. The striking cloud-shaped gallery has been designed to twist in the middle, echoing the curves of a Rodin sculpture, Mr Slim explains.

The shining silver structure will be covered with 16,000 hexagonal pieces to catch the light, and is the centrepiece of a $750 million development at Plaza Carso, revitalising a previously rundown and dangerous northern part of the city.

“He is a great architect – very young, but very talented. I put him in charge of it,” Mr Slim explains of his son-in-law. “And then I told him: there are two architects on this project. He said who? And I said: you and me!”

It was not bluster. The businessman is obsessive with every detail of his gallery. The marble floor tiles have been brought from Greece, and he proudly points out that they are of exceptionally high quality without imperfections in the stone.

“It’s his hobby, his obsession,” says Eduardo Solar, the project supervisor. “Every day he comes in here with new ideas, checking that everything is perfect. His attention to detail is incredible.”

Aida Pavón, the construction manager, points out a speck of paint on a wall. “Yesterday he was in here and spotted that, and said it wasn’t good enough. I just see him come in and watch his eyes scanning the building, because I know that wherever his gaze settles, he is going to want something improving or tweaking.”

Mr Slim has already chosen the position of his favourite work – The Thinker, which now sits inside the vestibule, covered in bubble-wrap, contemplating the army of hard-hatted workers who scurry past to finish the project in time.

Facing that will hang another favourite: a giant mural – Naturaleza Muerta – by the Mexican Rufino Tamayo.

His late wife was a particular admirer of Rodin – one of the earliest pieces the couple bought was Rodin’s Mask of the Man with the Broken Nose – and Mr Slim has eagerly adopted her enthusiasm for the French sculptor.

“Rodin is one of the greatest sculptors in history, in all humanity. And they are amazing sculptures.

"He is a great, and he rediscovered – well, not rediscovered, that wasn’t necessary – but he didn’t depend so much on classic art, which has been very influential, but he was inspired by Michelangelo. They are very strong, the expression is very strong. He is one of the greatest.”

Mr Slim refuses to discuss the value of his collection, or individual works, but the museum’s director said that the most valuable piece was probably from da Vinci’s studio, Madonna dei Fusi (Madonna of the Yarnwinder).

The Duke of Buccleuch had his version of the painting stolen from his Scottish castle in 2003; its value was estimated at between £30-£50 million.

Mr Slim oversees all the purchases. While he has bought some entire collections from people who want their selection to remain intact – on the table in his office, a handwritten note offers him the chance to inspect a collection of Diego Riveras for sale – he bought most of the European works one by one.

“The auctioneers send me the catalogues, and so I go through them and chose the works.”

And if he could add one work to the collection?

“I don’t necessarily think it’s important to belong to the collection – just that it can be appreciated. Many sculptures aren’t lent much. But there are an innumerable number of sculptures that would be a dream for any museum. The Winged Victory of Samothrace, or Venus di Milo. Some great Greek sculptures. Some bronzes.

“Another of my favourites is a reproduction of Pieta, which is from the 20th century. They made two copies, and this is number three. The original is in the Vatican. It is going to be, from what I understand, the first time that this has ever been exhibited in a museum.”

With such an extensive and personal collection, Mr Slim admits that sometimes he comes in at night to wander the museum, and see his works unobstructed. “They are there to be enjoyed.”

It is now night-time at the museum’s site, and still the construction team are working on the final touches. It is also a Monday which, every week, means dinner with the family. So it is time for us to leave.

Mr Slim stands outside the gallery, named after his late wife, housing a collection that had been directed by his daughter, in a building designed by his son-in-law.

In a few days this highly personal project will open its doors to anyone who wants to enter, for free, and share Mr Slim’s pleasure in great works.

“I believe that we have to find means for all desirable things to be universally accessible. Culture. Entertainment. Sport. Communication. Health. Food. Housing. The fundamental things.”

“I was at Windsor Castle not that long ago,” he muses. “And I had forgotten how many amazing drawings are there, especially the da Vincis.